Many papers suggest having a minimum error degree of freedom of 12. When a new crop variety is evaluated for agronomic performance with a local check or control, number of replications needed to generate a degree of freedom value of 12 is 13. That is, number of treatments (n-1) X number of replications (r-1), which is (2-1)X(13-1). I maintain this minimum degree of freedom for experiments with three or more treatment, however I not sure in the case of a paired field experiment. I would be grateful for your support and suggestions.
@ Mamerto Reyes Hernández, Thank you for your answer and efforts in two languages. However, may be my question wasn't clear and the answer I am looking for is for the following. When comparing two varieties of a crop in a paired experimental design with an intention to deduce statistical inferences, what is the acceptable number of replications required? This would allow me to understand whether or not error degree of freedom computed should be 12 after undergoing a paired t-test statistical analysis. The outcome would then facilitate in inferring valid result to make scientific decision. Best regards
@ Mamerto Reyes Hernández, thank you very much for you answer. However, I do not know the language in you have provided your valuable answer. Could it be possible for you to translate in English please? Or someone who knows that language could please translate. Thank you
Sorry, I doubt that there is a standard sample size for this, I suspect it would just be bad statistics in any case. That might make some government agency happy, but would be meaningless. If you want to have enough power to detect a difference in yield, you must define that difference for a paired t test. Then you need a variance (or standard deviation) for that crop in your immediate area, climate and soil. Then, you will need to specify alpha and betta.
However, with a tiny loss in power, you could use Wilcoxon's paired sample test. Then you would only need to specify the minimum reasonable difference you seek as well as alpha and beta. I will leave looking up the calculation details to you,
My book has the details,
Research Decisions and Estimation With Confidence and Power: Up To Date Text and Reference From Classical and Recent Literature. ISBN-13: 978-1532721076, LCCN 2021913804
but my primary source for the sample size was:
Noether, Gottfried E. 1987. Sample size determination for some common nonparametric tests. J. of the Am. Statistical Association. 82:398. Theory and Methods.
PS: I haven't spoken Spanish since I was very young and I am now very old, But, Mamerto Reyes Hernández seems to be providing a similar answer and warning.
@ Lewis Maccarter, Thank you very much for your invaluable answer. Indeed, with your clarification, I can now conduct paired experiment and analyze data with confidence and in a statistically valid manner. I appreciate your time, for providing the reference and all the details Best wishes and have a wonderful time.
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